Quiz Maths Terminale : Testez vos connaissances en analyse et probabilités

Question 1 sur 10 10:00

[{"id":73992,"question":"Quelle est la dérivée de la fonction f(x) = 3x² + 2x - 5 ?","option_a":"6x + 2","option_b":"3x² + 2","option_c":"6x + 2x","option_d":"3x + 2","option_e":"","option_f":"","bonne_reponse":"A","explication":"La dérivée d'une fonction polynôme se calcule terme à terme : (3x²)' = 6x, (2x)' = 2, et (-5)' = 0. Donc f'(x) = 6x + 2.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73993,"question":"La fonction exponentielle est toujours positive sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"Pour tout réel x, eˣ \u003E 0. C'est une propriété fondamentale de la fonction exponentielle.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73994,"question":"Quelle est l'intégrale de f(x) = 2x + 1 entre 0 et 2 ?","option_a":"6","option_b":"4","option_c":"5","option_d":"3","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'intégrale se calcule en trouvant une primitive : F(x) = x² + x. On évalue F(2) - F(0) = (4 + 2) - (0 + 0) = 6.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73995,"question":"Dans une loi normale centrée réduite, quelle est la probabilité P(-1 ≤ Z ≤ 1) ?","option_a":"0,68","option_b":"0,95","option_c":"0,99","option_d":"0,34","option_e":"","option_f":"","bonne_reponse":"A","explication":"Environ 68 % des valeurs d'une loi normale centrée réduite se situent dans l'intervalle [-1, 1].","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73996,"question":"La suite définie par uₙ = (-1)ⁿ est convergente.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La suite alterne entre -1 et 1 et ne tend pas vers une limite unique. Elle est donc divergente.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73997,"question":"Quelle est la limite de la fonction f(x) = (x² - 1)\/(x - 1) quand x tend vers 1 ?","option_a":"0","option_b":"1","option_c":"2","option_d":"∞","option_e":"","option_f":"","bonne_reponse":"B","explication":"On factorise le numérateur : (x² - 1) = (x - 1)(x + 1). La limite devient (x + 1) = 2 quand x → 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73998,"question":"Dans une expérience aléatoire, si A et B sont deux événements incompatibles, alors P(A ∪ B) = P(A) + P(B).","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"A","explication":"C'est une propriété fondamentale des probabilités pour des événements incompatibles (P(A ∩ B) = 0).","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":73999,"question":"Quelle est la solution de l'équation différentielle y' = 2y avec y(0) = 3 ?","option_a":"y = 3e²ˣ","option_b":"y = 3eˣ\/²","option_c":"y = 3 + 2x","option_d":"y = 6eˣ","option_e":"","option_f":"","bonne_reponse":"A","explication":"La solution générale est y = Ce²ˣ. Avec y(0) = 3, on trouve C = 3. Donc y = 3e²ˣ.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74000,"question":"La fonction f(x) = x³ - 3x est croissante sur ℝ.","option_a":"Vrai","option_b":"Faux","option_c":"","option_d":"","option_e":"","option_f":"","bonne_reponse":"B","explication":"La dérivée f'(x) = 3x² - 3 s'annule en x = ±1. La fonction est décroissante entre -1 et 1.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0},{"id":74001,"question":"Quelle est l'espérance d'une variable aléatoire suivant une loi binomiale B(n=10, p=0,3) ?","option_a":"3","option_b":"0,3","option_c":"10","option_d":"7","option_e":"","option_f":"","bonne_reponse":"A","explication":"L'espérance d'une loi binomiale est E(X) = n × p = 10 × 0,3 = 3.","points":1,"type":"qcm","actif":1,"section_id":null,"ordre":0}]